Also new to the board are Bruce Black, representing the Military Officers Association of America; Dr. Holly Abernethy, representing the hospital's medical staff; and Karen Morrison, representing the hospital's Auxiliary organization.
San Juan Regional announced the changes Tuesday.
"I've always been supportive of the hospital and providing the best health care in San Juan County," said Atkinson.
Atkinson said he had been "very involved" with the hospital during his more than 30 years in county government. He said he looks forward to learning about how health care is changing, particularly with the implementation of the Affordable Care Act, which is popularly known as ObamaCare.
"I have concerns over where health care is going with the new laws," he said.
Sandy Williams, who serves as board chairwoman, said the new members bring a variety of different skills.
"I'm excited to work with these new people," she said. "I think they're going to fit in really well."
She said Atkinson's government experience should prove valuable.
"He understands the workings between the hospital and the county and how the finances work," Williams said. "I think he'll be a real plus in the future in helping with those things and also issues at the state level.
Stepping down after three-year terms are Dr. Dwayne Gibbs, former chief of staff; Richard Menning, former auxiliary representative; and James Shaheen, former treasurer.
The board helps with the hospital's strategic planning and oversees the chief executive, Rick Wallace.
Continuing members of the 2013-14 board are Williams, Charlene Scott, Christian Moore, Janel Ryan, Joseph Rasor, Jeff Bowman, Dr. Jack Eberhart, Dr. Charles Hoffman and Michael A. Jakino.